How to Make It
Season pork with 1 1/2 teaspoons salt and 3/4 teaspoon pepper. Place pork, fat side up, on a rimmed baking sheet; let stand at room temperature 30 minutes.
Preheat oven to 450°F. Roast pork in preheated oven until fat is lightly browned, about 15 minutes. Reduce oven temperature to 375°F without opening oven door. Continue cooking until an instant-read thermometer inserted in thickest portion registers 135°F, 25 to 30 minutes. Transfer pork to a platter, and let cool completely, about 1 hour. Cover with aluminum foil, and refrigerate until chilled, about 2 hours.
Process mayonnaise, tuna, lemon juice, 1 teaspoon salt, and 1/2 teaspoon pepper in a food processor until very smooth, about 30 seconds.
Toss together lettuces, tomatoes, carrots, cucumbers, and radishes in a large bowl; season with remaining 1 teaspoon salt and remaining 1/4 teaspoon pepper. Untie pork, and cut against the grain into 1/8-inch-thick slices. Serve pork and salad with tonnato sauce.